1. Field of the Invention
The present invention relates to a method and apparatus for deriving interval velocities and more particularly to methods for deriving the correct interval velocity from observed residual moveout in post migrated parts.
2. Related Prior Art
When seismic data is sorted into common-offset panels, each offset can be processed as if it were an individual seismic section. Common-offset depth migration converts each offset panel into a depth section, each of which represent the same subsurface structure. With a perfect velocity model, each offset section will yield identical images. For real seismic data, it is normally impossible to obtain a perfect velocity model and the migrated offset sections are different.
When these common-offset depth sections are sorted into common midpoint (CMP) gathers, differences in the images with offset can be readily seen. There are three post-migration parts (PMP's- migrated common offset depth sections sorted into common midpoint gathers) displayed in FIGS. 1A through 1C. Near offset traces are to the right.
In FIG. 1A, the velocity above the reflector is correct (4900 ft/sec). A flat-imaged event indicates that the reflector was depth migration to the same depth at each offset and, hence, the velocity model used in the migration is correct. In FIG. 1B, it is 5150 ft/sec, 250 ft/sec too high, and the image shows an increase in depth with offset. In FIG. 1C, the velocity is 4650 ft/sec, 250 ft/sec too slow, and the image shows a decrease in depth with offset.
FIG. 2 is a display of a migrated depth section obtained with a velocity model that is correct for reflector A and B but too slow for reflector C. In FIG. 3, the PMP at shot point 8274 is displayed. Near offset traces are to the left. It can be observed that event A and B correspond to flat images. Thus, it can be seen that the interval velocities above these reflectors are correct. Event C, on the other hand, corresponds to an image which decreases in depth with offset. Thus, it appears that the velocity above this reflector is too slow.
The common method of determining the correct velocity above reflector C is to migrate the data with several velocities until one is found which produces a flat image. This repetitive migration method, even though accurate, is time consuming and expensive.
There are many methods in the prior art for processing seismic data which require the determination of velocity. For example, U.S. Pat. Nos. 4,766,574 illustrates the alignment of seismic data migrated before stack but still requires a velocity determination.
U.S. Pat. No. 4,766,574 titled "Method for Depth Imaging Multicomponent Seismic Data, (Norman D. Whitmore, Jr., et al.), relates to a method of migrating time dependent reflectivity functions prior to stacking to obtain depth images of the earth's subsurface geological structure as well as estimates of shear and compressional wave interval velocities. Measures are obtained of generated seismic wavefields incident on reflecting interfaces or subsurface layer boundaries in the earth's crust. Measures are also obtained of resulting seismic wavefields scattered from these interfaces. The incident and scattered seismic wavefields are employed to produce time-dependent reflectivity functions representative of the reflecting interfaces. By migrating these time-dependent reflectivity functions, depth images of the reflecting interfaces can be obtained. For pairs of multicomponent seismic data, the dyadic set of multicomponent seismic data are partitioned so as to separate the variously coupled incident and reflected wavefields in the recorded multicomponent seismic data. The incident and reflected wavefields are cross-correlated to form time-dependent reflectivity functions. These time-dependent reflectivity functions are then iteratively migrated according to a model of wavefield velocities of propagation to obtain better estimates of the compressional and shear wave interval velocity. The migrated reflectivity functions can then be stacked to produce better depth images of the earth's subsurface geological structures.
Other methods may be used for migration but again, velocity is necessary. The following patents illustrate methods of migrating seismic data treating velocity determination in different stages.
U.S. Pat. No. 4,745,585, "Method of Migrating Seismic Data" (Kenneth L. Larner), relates to seismic data which is passed through a preselected number of migration stages. During each stage, data is migrated a plurality of times, where the migration-velocity function is a minor fraction of the velocity required to fully migrate the data in a single stage. The cascaded migration migrates data having steeply-dipping events with what is alleged to be greater noise reduction than does a single-stage migration.
U.S. Pat. No. 4,813,027 titles "Method and Apparatus for Enhancing Seismic Data" (Hans Tieman) relates to a method and apparatus for stacking a plurality of seismic midpoint gathers to provide a pictorial representation of seismic events. The approximate propagation velocity, corresponding to a selected event in a common midpoint gather, is determined by summing the common midpoint gather using first and second weights to provide respective first and second weighted sums over an offset based on an estimated velocity corresponding to the event. A velocity error value indicative of the approximate error between the estimated velocity and the actual velocity is developed from the sums. The common midpoint gather is then restacked in accordance with the determined propagation velocity to provide an enhanced pictorial representation of the seismic event. The first and second weighted sums are taken over a time window centered upon an estimated zero offset travel time for the event. The first and second weights can be selected to provide rapid, slow or intermediate convergence upon the true velocity. The velocity error value is determined as a function of the deviation of the peak of the first weighted sum from the center of the time window, relative to the deviation of the peak of the second weighted sum from the center of the time window. Alternatively, the velocity error value is determined as a function of the deviation of the peak of the cross-correlation of the first and second weighted sums from the center of the time window.
U.S. Pat. No. 4,241,429 titled "Velocity Determination and Stacking Process from Seismic Exploration of Three Dimensional Reflection Geometry" (Marvin G. Bloomquist et al) relates to a method for determining the dip and strike of subsurface interfaces and average propagation velocity of seismic waves. In seismic exploration, linear, multiple fold, common depth point sets of seismograms with three dimensional reflection geometry are used to determine the dip and strike of the subsurface reflecting interfaces and the average velocity of the path of the seismic energy to the reflecting interface. The reflections in each set appear with time differences on a hyperbola with trace spacings determined by the source receiver coordinate distance along the lines of exploration. The offset of the apex of this hyperbola is determined from a normal moveout velocity search of the type performed on two dimensional common depth point (CDP) sets. This search identifies the correct stacking velocity and hyperbola offset which are used to determine dip, strike and average velocity.
U.S. Pat. No. 4,802,146 titles "Method for Movement Correction and Stacking Velocity Estimation of Offset VSP Data" (George P. Moeckel) relates to a moveout correction process and stacking velocity estimation process to permit stacking of vertical seismic profile (VSP) data. The primary reflection time is determined by using the two-way travel time, the root mean square velocity of acoustic pulses in the formation and the first arrival time of direct path acoustic pulses.
U.S. Pat. No. 4,736,347 titled "Multiple Stacking and Spatial Mapping of Seismic Data" (Bernard Goldberg et al.) relates to a method for determining the dip of subsurface formations and the apparent acoustic velocity. Seismic traces are stacked in a plurality of orthogonal measures to form multiple stacked traces at a positive offset. The stacking process determines the apparent velocities as functions of the travel time at the positive offset. The interval acoustic velocity of the first layer is then determined from knowledge of surface topography, source-receiver offset, two-way travel times and the first reflector apparent velocities. The first layer velocity information enables the incident and emergent angles of the raypaths at the surface to be calculated, as well as enabling the dip angles and spatial coordinates of the reflection points on the first reflecting boundary to be determined. Seismic data corresponding to the second reflecting boundary are then mapped spatially to the first reflecting boundary by ray tracing and by calculating the apparent velocities at the first boundary. The process is repeated for each succeedingly deeper boundary. The derived acoustic velocity model of the earth is displayed as a stacked seismic section in spatial coordinates. This process may be applied to obtain earth models and seismic sections in both two and three dimensions.